Consider the SIGN CHANGE problem. We own a business with a big sign above it, and we need to change the name. It costs $10 to change a letter, and $25 to delete a letter - importantly, it is not possible to insert a new letter. We want to find the minimum cost to do this. For example, a sign saying "HELLO WORLD" can be changed to "YELLOWORC" for $70: replace "H" with "Y", delete the space, replace "L" with "C", and then delete the "D". Suppose X = x_1 x_2 ... x_n is the old sign, and we want to change it to Y = y_1 y_2 ... y_m. Note that 0 lessthanorequalto m lessthanorequalto n. Define a subproblem SC(i, j) as the minimum cost to convert x_i ... x_n to y_j ... y_m. Give a recurrence relation for SC. Include the base cases